Extensive transport measurements have been completed on deep and shallow-channelled InGaAs p-HEMTS of varying growth temperature, indium content, spacer thickness and doping density, with a view to thorough characterisation, both in the metallic and the localised regimes. Particular emphasis was given to MBE grown layers, with characteristics applicable for device use, but low measurement temperatures were necessary to resolve the elastic scattering mechanisms. Measurements made in the metallic regime included transport and quantum mobility - the former over a range of temperatures between 1.5K to 300K. Conductivity measurements were also acquired in the strong localisation regime between about 1.5K and 100K.Experimentally determined parameters were tested for comparison with those predicted by an electrostatic model. Excellent agreement was obtained for carrier density. Other parameters were less well predicted, but the relevant experimental measurements, including linear depletion of the 2DEG, were sensitive to any excess doping above a 'critical' value determined by the model. At low temperature (1.5K), it was found that in all samples tested, transport mobility was strongly limited at all carrier densities by a large q mechanism, possibly intrinsic to the channel. This was ascribed either to scattering by the long-range potentials arising from the indium concentration fluctuations or fluctuations in the thickness of the channel layer. This mechanism dominates the transport at lower carrier densities for all samples, but at high carrier density, an additional mechanism is significant for samples with the thinnest spacers tested (2.5nm). This is ascribed to direct electron interaction with the states of the donor layer, and produces a characteristic transport mobility peak.